We've had some issues with changing GET to POST in the past and had to go back (#16335, #18094).

Perhaps it's an edge case, but changing to POST here will re-introduce an issue similar to the one in #18094 for no-JS. Searching and filtering would be broken when navigating between pages if there are more themes found than the default per_page limit, which is 36 ([21768]).

An alternative solution would be to reset $_SERVER['REQUEST_URI'] to avoid the pollution of _wp_http_referer. We already do that in plugins.php and several other files: tags/3.6/wp-admin/plugins.php#L23​.